The Rangers ended a four-game losing streak, their longest of the season and one that coincided with the absence of Nash.
Nash sat out all four of those losses with an undisclosed injury and he peppered the Tampa Bay goal with 12 shots in his comeback. Just one of those got through and it produced the last of the New York goals with 1:33 to play.
Carl Hagelin and Derek Stepan gave New York the lead with goals 1:17 apart in the first period and Marc Staal's power-play goal in the second period gave the Rangers a 3-1 lead.
The only Tampa Bay goal came from Martin St. Louis with 3:51 to go in the first period.
New York had 42 shots overall against Mathieu Garon. Tampa Bay has lost three in a row.